Fast and memory efficient encoding of sound objects using spherical harmonic symmetries

ABSTRACT

A method of encoding sound objects includes receiving a set of monophonic sound inputs. Each of the set of monophonic sound inputs includes position and orientation information of a sound object relative to a source position. The set of monophonic sound inputs are encoded into a higher order ambisonic (HOA) sound field in a spherical harmonics domain based on a spherical harmonics dataset including a subset of all spherical harmonic coefficients for a given subset of azimuth and elevation angles. Some embodiments include decoding the HOA sound field to generate a set of loudspeaker signals.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is related to U.S. Provisional Patent Application62/550,383, entitled “FAST AND MEMORY EFFICIENT ENCODING OF SOUNDOBJECTS USING SPHERICAL HARMONIC SYMMETRIES” and filed on Aug. 25, 2017,the entirety of which is incorporated by reference herein.

BACKGROUND

As the web and mobile devices emerge as virtual reality (VR) andaugmented reality (AR) platforms for delivering content, spatial audiowill play an increasing role in the user's experience. For virtualscenes to be perceived as immersive, visual imagery should beaccompanied by spatial audio to present realistic VR experiences.Spatial audio allows the perception of sounds that can come from anydirection, and that are associated in 3D space with audio sources, thusenveloping the user in 360-degree sound. The usage of spatial audiohelps draw the user into a scene and creates the illusion of entering avirtual world as presented in VR/AR.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood, and its numerousfeatures and advantages made apparent to those skilled in the art byreferencing the accompanying drawings. The use of the same referencesymbols in different drawings indicates similar or identical items.

FIG. 1 is a diagram illustrating audio processing for encoding of soundobjects into Higher Order Ambisonic (HOA) sound fields and decoding ofHOA sound fields into binaural stereo signals in accordance with someembodiments.

FIG. 2 is a diagram illustrating spherical harmonic basis functions inaccordance with some embodiments.

FIG. 3 is a diagram illustrating a sound object rendering pipeline forperforming binaural rendering in the spherical harmonics domain inaccordance with some embodiments.

FIG. 4 is a diagram illustrating virtual microphone patterns producedusing different Ambisonic decoders in accordance with some embodiments.

FIG. 5 is a graph illustrating gain values to be applied to eachAmbisonic channel of a given Ambisonic order in accordance with someembodiments.

DETAILED DESCRIPTION

Higher Order Ambisonics (HOA) refers to a set of spatial audiotechniques for capturing, manipulating and reproducing sound scenes,based on a spherical Fourier expansion of the sound field. Ambisonicsound fields have an “order” which corresponds to the level of spatialdetail provided. The order determines the number of channels present—newchannels are added on each time the order is increased. At “zero” order,there is just one mono channel. At first order, as described above,there are three additional spatial channels (totaling four), eachbehaving like a figure-of-eight microphone. At second order, anotherfive channels are added (totaling nine), and so on. It will beappreciated that the channels correspond to the spherical harmonicswhich arise in solutions to the Acoustic Wave Equation in sphericalpolar coordinates.

Some approaches to spatial audio coding (e.g., surround-sound coding)include scene-based audio, which involves representing a sound fieldusing coefficients of spherical harmonic basis functions. Suchcoefficients are also called “spherical harmonic coefficients” or SHC.Higher Order Ambisonics (HOA) offers the advantage of representing acomplete sound field in the vicinity of a specific location inthree-dimensional (3D) space. Such HOA representation is independent ofany specific loudspeaker set-up, in contrast to techniques such asstereo- or surround-sound. However, this flexibility is at the expenseof computational resources related to a decoding process required forplayback of the HOA representation particular to different loudspeakersetups.

FIGS. 1-5, as described in further detail below, illustrate techniquesfor digital signal processing (DSP) for the encoding and decoding ofbinaural sound sources. In some embodiments, a method of encoding ofsound objects into HOA sound fields includes receiving a set ofmonophonic sound inputs, wherein each of the monophonic sound inputsincludes position and orientation information of a sound object relativeto a source position (e.g., a center of a sphere). The set of monophonicsound inputs are encoded, based on a spherical harmonics lookup tableincluding a subset of all spherical harmonic coefficients for a givensubset of azimuth and elevation angles, into a higher order ambisonic(HOA) sound field in a spherical harmonics domain. A binaural soundoutput is generated by decoding the HOA sound field to generate a set ofloudspeaker signals and convolving two or more of the generated sets ofloudspeaker signals and summing a left channel signal and a rightchannel signal. In some embodiments, the spherical harmonics lookuptable is computed prior to performing sound object encoding. Forexample, the computing of the spherical harmonics lookup table includescomputing a first sphere quadrant of all spherical harmoniccoefficients. Afterwards, a SHC of a second sphere quadrant is retrievedfrom the spherical harmonics lookup table based on a symmetry look-uptable containing SHC symmetry information. Further, to control sourcesound spread, a gain correction is applied to each of a plurality ofAmbisonic channels of the HOA sound field to change a source spread ofthe sound object and an energy-preserving gain correction is applied toeach of a plurality of Ambisonic channels of the HOA sound field tomaintain a total energy level of the HOA sound field.

FIG. 1 is a diagram illustrating audio processing for encoding of soundobjects into Higher Order Ambisonic sound fields in accordance with someembodiments. As shown, an audio processing pipeline 100 includes aplurality of monophonic (hereinafter, “mono”) sound sources 102 providedas input signals into the audio processing pipeline 100. As used herein,the mono sound sources include, but are not limited to: directional(i.e., single channel) sound recordings, such as sharply parabolic soundrecordings; sound recordings with discrete or nearly-discrete spatialdirection; sound recordings where actual spatial information isconstrained to a discrete or nearly-discrete spatial direction; soundrecordings where actual spatial information is disregarded and replacedby artificially generated spatial information; and, as for example in avirtual reality environment, a generated sound with a virtual sourceposition and direction. Further, any sound source may be interpreted asa monophonic input signal by disregarding any known spatial informationfor an actual (i.e., recorded) sound signal treating it as a monophonicsignal which can then be associated with generated spatial information.

Each mono sound source 102 is provided along with source information104, which includes source position and orientation information formodeling acoustic sound sources, to an encoder 106. In some embodiments,the source information 104 for each mono sound source 102 includesassociated spatial object parameters, which positions the mono soundsource 102 in a Cartesian coordinate system relative to an originposition (e.g., center of a room or other user-defined origin in thevirtual environment that the listener is in).

In various embodiments, the operations of encoder 106 includes encodingaudio channels (e.g., mono sound sources 102) into an Ambisonics format,AmbiX, A-format, or other higher-order Ambisonics for representingthree-dimensional sound fields. Ambisonics is a full-sphere surroundsound technique that covers sound sources above and below the listener,in addition to the horizontal plane. Unlike other multi-channel surroundformats, Ambisonics transmission channels do not carry speaker signals.Instead, Ambisonics transmission channels contain a speaker-independentrepresentation of a sound field, which is later decoded according to alistener's particular speaker setup. This offers the listener aconsiderable degree of flexibility as to the layout and number ofspeakers used for playback.

In some embodiments, the audio processing pipeline 100 uses the AmbiXAmbisonics convention for encoding and decoding of sound objects. TheAmbiX convention imposes the use of Schmidt semi-normalization (SN3D)and Ambisonic Channel Number (ACN) sequencing of spherical harmonics. Inthe spatial audio field for Ambisonics, the terms “order” is usuallydenoted as n (also referred to as Ambisonic order) and “degree” isusually denoted as m (also referred to as Ambisonic degree). WithAmbisonics, the 3D spherical coordinate system is normally set up sothat X-axis direction is forwards, Y-axis direction is to the left, andZ-axis direction is upwards. The conversion between spherical andCartesian coordinates is defined by the following equations:

$\begin{matrix}{x = {{\overset{\rightarrow}{r}}\cos\;\phi\;\cos\;\theta}} & (1) \\{y = {{\overset{\rightarrow}{r}}\sin\;\phi\;\cos\;\theta}} & (2) \\{z = {{\overset{\rightarrow}{r}}\sin\;\theta}} & (3)\end{matrix}$where ϕ is the azimuth angle with an anti-clockwise rotation and θ isthe elevation angle calculated from the x-y plane.

The encoder 106 receives data representative of room acoustic properties108 and listener position/orientation information 110. Directionalcomponents of room reverberation (i.e. early reflections) can be encodedinto an Ambisonic sound field, similarly as other discrete soundsources. The room acoustic properties 108 controls characteristics ofspatial reflections and reverberation, and the listenerposition/orientation information 110 provides listener position at themoment of encoding, thereby modeling a physical listener of the variousmono sound sources 102. In some embodiments, the encoder 106 encodes oneor more mono sound sources 102 in an Ambisonics output 112 (e.g., anAmbisonic sound field b) by multiplying a monophonic pressure signalcorresponding to the sound source s by a vector Y with sphericalharmonic coefficients Y_(n) ^(m)(ϕ, θ), as represented by the followingequation:b=sY  (4)

The spherical harmonic coefficients are defined by the followingequation:

$\begin{matrix}{{Y_{n}^{m}\left( {\phi,\theta} \right)} = {N_{m}^{m}{P_{n}^{m}\left( {\sin(\theta)} \right)}\left\{ \begin{matrix}{\cos\left( {{m}\phi} \right)} & {{{if}\mspace{14mu} m} \geq 0} \\{\sin\left( {{m}\phi} \right)} & {{{if}\mspace{14mu} m} < 0}\end{matrix} \right.}} & (5)\end{matrix}$where ϕ is the sound source horizontal angle and θ is the sound sourcevertical angle. Thus, the spherical harmonics are represented by Y_(n)^(m) (θ, ϕ) in angular direction (θ, ϕ), in which θ denotes thelongitudinal coordinate and ϕ denotes the latitudinal coordinate.Further, n is the Ambisonic order, m is the Ambisonic degree, and P_(n)^(|m|) are the associated Legendre functions (with the Condon-Shortleyphase undone). N_(n) ^(|m|) is the SN3D normalization term, which isdetermined according to the following equation:

$\begin{matrix}{N_{m}^{m} = \sqrt{\left( {2 - \delta_{m}} \right)\frac{\left( {n - {m}} \right)!}{\left( {n + {m}} \right)!}}} & (6)\end{matrix}$In some embodiments, the encoder 106 skips the

$\frac{1}{4\pi}$term in the normalization, thereby preserving the original sourceamplitude in the zeroth order spherical harmonic.

In general, the encoder 106 generates an Ambisonics output 112 (e.g., anambisonic sound field) that can then be rendered for listening. Theencoder 106 generally includes two parameters, azimuth and elevationangle, and distributes the mono sound sources 102 to the Ambisonicscomponents such that, when decoded, the sources will appear at desiredlocations. For example, as illustrated in FIG. 1, the mono sound sources102 are encoded into a first-order Ambisonics signal having fourchannels: W, X, Y and Z. In some embodiments, as discussed furtherbelow, the encoder 106 also includes a spread parameter related to anapparent size (e.g., width) of a sound source.

The W channel is the non-directional mono component of the ambisonicsoutput 112, corresponding to the output of an omnidirectionalmicrophone. The X, Y and Z channels are the directional components inthree dimensions, which correspond respectively to the outputs of threefigure-of-eight microphones, facing forward, to the left, and upward.The W channel corresponds to the sound pressure at a point in space inthe sound field whilst the X, Y and Z channels correspond to the threecomponents of the pressure gradient.

The four Ambisonic audio channels do not correspond directly to speakerfeeds. Instead, the channels contain components of the sound field thatare combined during a later decoding step. That is, loudspeaker signalsare derived by using a linear combination of the Ambisonic audiochannels, where each signal is dependent on the actual position of thespeaker in relation to the center of an imaginary sphere the surface ofwhich passes through all available speakers. Accordingly, the Ambisonicaudio channels can be decoded for (or combined to produce feeds for) anyloudspeaker reproduction array. Ambisonic sound fields allowmulti-channel audio to be generated, recorded and transferred from placeto place without worrying about the speakers that are going to be usedfor playback in the end. Ambisonic sound fields support full 3D too, asit captures essentially equal information in all directions and can berotated quite easily. This makes it useful for VR and AR applications,because Ambisonic sound fields can be rotated into place beforedecoding, depending on where the user's head is pointing.

In some embodiments, the Ambisonics output 112 (e.g., Ambisonic soundfield) is rendered using binaural decoder 116 to generate stereo output.That is, the multi-channel audio of the Ambisonics output 112 is decodedto 3D binauralized sound (e.g., a stereo track) for listening onregular, LR headphones. In one embodiment, the binaural decoder 116multiplies the Ambisonic signal b by the inverse of the loudspeakerre-encoding matrix L, which encodes i^(th) loudspeaker direction in thespherical harmonics, as represented by the following equation:

$\begin{matrix}{L = \begin{bmatrix}{Y_{0}^{0}\left( {\Phi_{1},\theta_{1}} \right)} & {Y_{0}^{0}\left( {\Phi_{i},\theta_{i}} \right)} & \ldots & {Y_{0}^{0}\left( {\Phi_{N},\theta_{N}} \right)} \\{Y_{1}^{- 1}\left( {\Phi_{1},\theta_{1}} \right)} & {Y_{1}^{- 1}\left( {\Phi_{i},\theta_{i}} \right)} & \ldots & {Y_{1}^{- 1}\left( {\Phi_{N},\theta_{N}} \right)} \\\vdots & \vdots & \vdots & \vdots \\{Y_{n}^{m}\left( {\Phi_{1},\theta_{1}} \right)} & {Y_{n}^{m}\left( {\Phi_{i},\theta_{i}} \right)} & \ldots & {Y_{n}^{m}\left( {\Phi_{N},\theta_{N}} \right)}\end{bmatrix}} & (7)\end{matrix}$where Φ_(i) is the azimuth angle of the i^(th) loudspeaker in the arrayand Θ_(i) is the vertical angle of i^(th) loudspeaker in the array.

The resulting loudspeaker signals g are obtained by the followingequation:g=Db  (8)where D is a Moore-Penrose pseudo-inverse of L, as represented by thefollowing equation:D=L ^(T)(LL ^(T))⁻¹  (9)

To reproduce Ambisonic sound fields binaurally, the audio processingpipeline 100 uses the concept of “virtual loudspeakers”, in whichloudspeaker signals are generated by decoding an Ambisonic sound field.In some embodiments, the binaural decoder 116 filters the resultingloudspeaker signals g with Head Related Transfer Functions (HRTFs)corresponding to the spatial locations of the virtual loudspeakers.Next, the binaural decoder 116 separately sums the left and rightchannel signals to generate a stereo binaural headphone signal. Forexample, to obtain the left and right ear headphone feed (e.g.,2-channel audio), the binaural decoder 116 performs a convolution basedon the following equations:y _(L)=Σ_(i=1) ^(N) h _(Li) *g _(i)  (10)y _(R)=Σ_(i=1) ^(N) h _(Ri) *g _(i)  (11)where h_(Li) and h_(Ri) are time-domain representations of the HRTFs(e.g., Head Related Impulse Responses or HRIRs, for left and rightchannels, respectively) corresponding to the i^(th) loudspeakerlocation, g_(i) is the i^(th) loudspeaker signal feed, and * denotes theconvolution process.

In various embodiments, the encoder 106 encodes the mono sound sources102 into a Higher Order Ambisonics (HOA) sound field by evaluating atruntime a number (e.g., 9, 16, or more) of higher order SphericalHarmonic (SH) functions at given azimuth and elevation angles. To avoidhigh computational cost of these evaluations, a lookup table withpre-computed SH values (e.g., SH coefficients table 114) is utilized.However, given a high spatial resolution of human hearing (e.g., 1degree), pre-computation and storage costs of such largemulti-dimensional tables would be prohibitively large for encoding HOAsignals. Accordingly, as described in further detail herein, the SHcoefficient table 114 more efficiently stores spherical harmonics basedon the symmetries of SH functions, thereby reducing storage andpre-computation costs.

FIG. 2 is a diagram illustrating spherical harmonic basis functions 200from the zero order (n=0) to the fourth order (n=4) in accordance withsome embodiments. In FIG. 2, the spherical harmonic basis functions 200are shown in three-dimensional coordinate space with both the order andthe degree shown. Based on the order (n) value range of (0,4), thecorresponding degree (m) value range of FIG. 2 is (−4,4). Sphericalharmonic functions can be symmetric against the x, y, and/or z Cartesianaxes. For example, the equation Y_(n) ^(m)(ϕ,θ)=Y_(n) ^(m)(−ϕ,θ)indicates that Y_(n) ^(m) (θ,ϕ) is symmetric with respect to thesagittal plane (e.g., left-right symmetry) but at the same time isanti-symmetric with respect to the horizontal plane (e.g., up-downanti-symmetry), and thus Y_(n) ^(m)(ϕ,θ)=(ϕ,−θ). A spherical harmonicwhich exhibits the above properties is, for example, spherical harmonicfunction 202 of FIG. 2, representing the spherical harmonic Y₁ ⁰(ϕ,θ)with ACN=2, which is front-back symmetric, left-right symmetric, butup-down anti-symmetric. It is also possible that a spherical harmonic isleft-right anti-symmetric, front-back anti-symmetric, and up-downsymmetric. For example, the equation Y_(n) ^(m)(ϕ,θ)=−Y_(n) ^(m)(ϕ,−θ)indicates that a spherical harmonic is left-right anti-symmetric,front-back anti-symmetric, and up-down symmetric if n and m are odd andwhen n=m, such as for spherical harmonic function 204 of FIG. 2,representing the spherical harmonic function Y₃ ³(ϕ,θ)

In general, symmetry and anti-symmetry-related sign flip for a givenspherical harmonic Y_(n) ^(m)(θ,ϕ) with respect to the y, z, and xCartesian axes, respectively, is represented by:

$\begin{matrix}{{\xi_{y}\left( {n,m} \right)} = \left\{ \begin{matrix}1 & {{{if}\mspace{14mu} m} \geq 0} \\{- 1} & {{{if}\mspace{14mu} m} < 0}\end{matrix} \right.} & (12) \\{{\xi_{z}\left( {n,m} \right)} = \left( {- 1} \right)^{n + m}} & (13) \\{{\xi_{x}\left( {n,m} \right)} = \left\{ \begin{matrix}\left( {- 1} \right)^{m} & {{{if}\mspace{14mu} m} \geq 0} \\{- \left( {- 1} \right)^{m}} & {{{if}\mspace{14mu} m} < 0}\end{matrix} \right.} & (14)\end{matrix}$where ξ represents a symmetry-related phase coefficient for therespective axes. Therefore, by pre-computing and storing only one spherequadrant of the spherical harmonic coefficients, the above symmetryinformation provides the basis for retrieving an arbitrary sphericalharmonic coefficient of the same order and degree.

In some embodiments, whether to employ a given phase coefficient dependson which quadrant to pre-compute as well as which quadrant the soundsource is located in. For example, with a pre-computed front-left-topquadrant

$\left( {0 \leq \left( {\phi,\theta} \right) \leq \frac{\pi}{2}} \right)$to retrieve a spherical harmonic coefficient for an arbitrary angle pairin the rear-right-bottom quadrant

$\left( {{{- \pi} \leq \phi \leq {- \frac{\pi}{2}}},{{- \frac{\pi}{2}} \leq \theta \leq 0}} \right),$the following is performed:Y _(n) ^(m)(ϕ,θ)=ξ_(y)(n,m)ξ_(z)(n,m)ξ_(x)(n,m)Y _(n)^(m)(π−|ϕ|,|θ|)  (15)

The audio processing pipeline, as described by the various embodimentsherein, applies similar logic to determine the spherical harmoniccoefficients for other sound source directions (e.g., in other spherequadrants), by dropping redundant symmetry-related phase coefficientsand constraining the horizontal angle to the

$\left\lbrack {0,\frac{\pi}{2}} \right\rbrack$range. In this manner, the audio processing pipeline computes a limitedsize look-up table of spherical harmonic coefficients in the

$\left\lbrack {0,\frac{\pi}{2}} \right\rbrack$range at 1° resolution, as well as a symmetry look-up table. Atrun-time, such as when performing sound object encoding, the encoderretrieves spherical harmonic coefficients from the look-up table toencode sound source direction into the Ambisonics output.

FIG. 3 is a block diagram illustrating an example sound object renderingdevice 300 for performing binaural rendering in the spherical harmonicsdomain in accordance with some embodiments. The sound object renderingdevice 300 includes any device capable of encoding audio data, such as adesktop computer, a laptop computer, a workstation, a tablet or slatecomputer, a dedicated audio recording device, a cellular phone(including so-called “smart phones”), a personal media player device, apersonal gaming device, or any other type of device capable of encodingaudio data. While shown as a single device, i.e., sound object renderingdevice 300 in the example of FIG. 3, the various components or modulesreferenced below as being included within the sound object renderingdevice 300, in various embodiments, forms separate devices that areexternal from the sound object rendering device 300. In other words,while described in this disclosure as being performed by a singledevice, i.e., the sound object rendering device 300 in the example ofFIG. 3, the techniques may be implemented or otherwise performed by asystem comprising multiple devices, where each of these devices may eachinclude one or more of the various components or modules described inmore detail below. Accordingly, the techniques should not be limited tothe example of FIG. 3.

The sound object rendering device 300 receives one or more mono soundsources 302 and provides the one or more mono sound sources 302 to anencoder module 304. The encoder module 304 encodes the one or more monosound sources 302 into a Higher Order Ambisonics (HOA) sound field(e.g., one of the sound fields 306) based on a number (e.g., 9, 16, ormore) of higher order spherical harmonic functions at given azimuth andelevation angles. Higher orders project onto more harmonics andtherefore have increased spatial resolution relative to lower orderAmbisonics, but also use more channels for the encoded signal. To avoidhigh computational cost of these evaluations, the sound object renderingdevice 300 utilizes a lookup table with pre-computed SH values (e.g., SHcoefficients table 308).

In one embodiment, the SH coefficients table 308 includes all sphericalharmonics pre-computed and stored up to the 3^(rd) order. To improvememory utilization optimization, in another embodiment, the SHcoefficients table 308 stores only (N-channel+1)² number of componentsfor azimuth angles ϕ: 0:1:90; elevation angles θ: 0:1:90 based on thesymmetries of spherical harmonics, as discussed above in more detailrelative to FIG. 2. The SH coefficients table 308 includes angleslimited to the upper/left/forward quadrant only and thus provides alookup table enabling more efficient storage and processing (e.g.,encoding) of spherical harmonic signals. Additionally, the sphericalharmonic coefficients may be computed to a higher order due to thereduced memory footprint resulting from storing a reduced number ofcomponents for the SH coefficients table 308.

In some embodiments, a transformation module 310 receives one or more ofthe sound fields 306 for performing one or more Ambisonicstransformation operations prior to decoding of the Ambisonics encodedsound fields 306. An Ambisonics transformation can be represented by thefollowing equation:{tilde over (b)}=Tb  (16)where a transformed Ambisonic signal vector {tilde over (b)} is obtainedby applying a matrix T to the Ambisonic input signal vector b (e.g., theone or more of the sound fields 306). For example, in variousembodiments, different types of transformations such as rotation may beapplied to the Ambisonic sound field.

Each individual sound object encoded into an Ambisonic representation isassumed to be dynamic such that its position relative to a listener'shead can change at an arbitrary rate and independently of other soundobjects. Hence, to re-position an individual sound object in 3D space,the individual sound object just needs to be re-encoded with updatedspherical harmonic coefficients. However, there are situations whererotating an Ambisonic sound field 306 is a better solution. For example,one such situation is when multiple sound objects in the Ambisonic soundfield 306 have already been encoded into the Ambisonic representationusing, for example, a microphone array.

In one embodiment, the transformation module 310 includes a rotator thatperforms a first order Ambisonic rotation that includes applying a 3×3rotation matrix to the velocity components of the sound field 306 whilekeeping the pressure component unmodified. This is equivalent to asimple vector rotation. In another embodiment, the transformation module310 includes a rotator that performs higher order Ambisonics rotationinvolving rotation of vectors with dimensionality higher than 3, such asby use of spherical harmonic rotation matrices computation by recursion.In other embodiments, the transformation module 310 includes modules forfocusing or warping the sound field, applying reverb effects, and thelike.

With the virtual loudspeaker reproduction approach discussed herein, thesound object rendering device 300 determines HRIRs corresponding to thespatial locations of an array of loudspeakers. For example, in someembodiments, a regular octagonal array of loudspeakers forms the arrayof loudspeakers. The sound object rendering device 300 measures HRIRscorresponding to spatial locations of all the loudspeakers required fora given decoder configuration and organizes the determined HRIRs into avirtual loudspeaker database (not shown). Subsequently, measurements areextracted from the virtual loudspeaker database for decoding/Ambisonicaudio rendering.

At run-time, the rendering module 312 receives an Ambisonic sound fieldas input (e.g., after encoding into the spherical harmonics domain bythe encoder module 304 and/or after transformation by the transformationmodule 310) and performs HRTF-based rendering of the sound field forlistening. For example, in some embodiments, the rendering module 312includes a binaural renderer (such as the binaural decoder 116 ofFIG. 1) that decodes the input signals with HRTFs corresponding to thespatial locations of the virtual speakers 312. The rendering module 312then convolves the decoded signals with HRIRs and sums left and rightchannel signals to generate the binaural output 314, thereby providingAmbisonic playback.

The sound object rendering device 300 reduces run-time complexity bypre-computing look-up tables for reducing pre-computation time andreducing the memory footprint associated with look-up tables, asdiscussed above. Real-time computation of SH coefficients (e.g., basedon equations (5) and (6) above) is computationally intensive.Accordingly, the sound object rendering device 300 pre-computes the SHcoefficients and stores the pre-computed SH coefficients in SHcoefficients table 308 as a Look Up Table (LUT) or other dataset toreduce run-time complexity while reducing the memory footprint andprecomputation initialization time. Thus, as described herein,symmetries of SH functions are exploited to efficiently pre-compute,store, and then index and retrieve the SH coefficients at run-time,thereby reducing the memory footprint required to store SH coefficientsin SH coefficients table 308 and increasing pre-computation speed.

In this manner, the sound object rendering device 300 encodes soundobjects into HOA sound fields and allows listeners to experience thesound objects to be coming from desired spatial locations (i.e.,encoding of sound source directions into the sound field). However,conventional Ambisonics rendering results in a constant angular spread(i.e., sound width) of the sound source depending on the Ambisonic orderand its spatial location with respect to the listener. This is alimitation, as real-life sound sources differ in terms of their sizes(e.g., size of the wings of a fly vs. engines on the wings of a plane).Changing the Ambisonic order of reproduction would result in a step-wisenarrowing or widening of a sound source depending on the Ambisonic orderof reproduction. However, these changes are often not feasible (forexample, when a fixed order Ambisonic decoder is used) or smooth changesare required. Additionally, changes to the Ambisonic order ofreproduction results in changes to relative energy ratios between soundfields thus leading to a sound object being perceived quieter or louder(or closer or more distant), which is undesirable.

In some embodiments, the sound object rendering device 300 furtherincludes shelf filters (not shown) and a spherical harmonics re-encoder(not shown) for modeling of sound source angular spread, which hasmultiple uses in sound design (for example, to simulate wide orvolumetric sound sources). As discussed further herein, the angularspread (i.e., width) of a sound object encoded into HOA sound fields canbe controlled in a smooth way while preserving its acoustic energy (andthus avoiding loudness fluctuations).

The angular spread of an Ambisonic sound source is related to the metricof a spread of its acoustic energy across a sphere, as represented bythe following equation:ϕ_(S)=arccos(∥{right arrow over (r _(E))}∥)  (17)

where ϕ_(S) is the angular spread (i.e., width) of the Ambisonic soundsource in radians and ∥{right arrow over (r_(E))}∥ is the magnitude ofan energy vector pointing in the direction of that Ambisonic soundsource. In various embodiments, the sound object rendering device 300utilizes the relationship of equation (17) above. However, the curve ismodified for very low values of ∥{right arrow over (r_(E))}∥ (e.g.,below Ambisonic order 1) so that the sound source spread reaches 2πinstead of

$\frac{\pi}{2}$when ∥{right arrow over (r_(E))}∥=0.

MaxRe decoding, such as described above relative to FIG. 3, maximizesenergy concentration in the direction of a sound source, thus minimizingits spread. For example, FIG. 4 is a diagram illustrating virtualmicrophone patterns produced using different Ambisonic decoders inaccordance with some embodiments. As shown, a third order basicAmbisonic decoder generates a sharper looking graph 402 than graph 404associated with a third order MaxRe Ambisonic decoder. The maximumtheoretical ∥{right arrow over (r_(E))}∥ for decoding based on a thirdorder basic HOA source is 0.75 (i.e., ϕ_(S)≈0.7227), corresponding to aspread of approximately 41.4°. However, the graph 402 includes visibleside lobes (which correspond to signal components at directions otherthan the direction of a sound source, representing out-of-phasesignals). The visible side lobes result in a wider overall energyspread, which translates to a wider source sound. The HOA source for thesame order MaxRe decoding has ∥{right arrow over (r_(E))}∥≈0.861 (i.e.,ϕ_(S)≈0.5336), corresponding to a source spread of approximately 30.6°.The MaxRe source maximizes energy concentration in the direction of thesound source, thus minimizing its spread and would be sharper.

As further described herein, the sound object rendering device 300controls the spread of the MaxRe source. Generally, to convert a basicHOA to a MaxRe HOA, the ratio of spherical harmonic coefficients in theAmbisonic signal is modified. In other words, width of a HOA soundobject can be modified by applying per-order gain coefficients G(n) tothe Ambisonic channels.

By knowing a desired spread for a given sound source, the relationshipof equation (17) can be inverted to determine the required ∥{right arrowover (r_(E))}∥ and thus the minimum required Ambisonic order n to createsuch a sound source. This relationship is approximated using anexponential curve as represented by the following equation:n=┌13.15e ^(−2.74ϕ) ^(S) ┐  (18)

By using MaxRe gain coefficients (instead of basic), the sound objectrendering device 300 achieves step-wise control over sound sourcespread. Step-wise control over sound source spread is achieved bymultiplying the higher order sound field input vector by a lower orderset of coefficients, which changes the relative energy ratios ofchannels of different orders and zeroes out higher order channelcontributions. The control of width of sound sources in a stepwisemanner by changing the MaxRe coefficients and zeroing of higher orderchannels is illustrated in graph 502 of FIG. 5. The graph 502illustrates gain values (i.e., MaxRe gain coefficients) that eachAmbisonic channel of a given order should be scaled by in order toobtain a MaxRe decoder of a given order. As shown, the curve 504corresponds to gain values to scale each Ambisonic channel of order 0,the curve 506 corresponds to gain values to scale each Ambisonic channelof order 1, the curve 508 corresponds to gain values to scale eachAmbisonic channel of order 2, the curve 510 corresponds to gain valuesto scale each Ambisonic channel of order 3, and the curve 512corresponds to gain values to scale each Ambisonic channel of order 4.

Smoothness of transitions between different source spreads (as opposedto keeping a constant angular spread) helps to simulate a virtual soundsource of a constant size in 3D space (e.g., a volumetric source). Fromthe point of view of the listener, a sound source has a different spreaddepending on its distance to the listener. To obtain smooth transitionsbetween different source spreads, in some embodiments, the sound objectrendering device 300 numerically determines the best polynomialapproximation of each MaxRe coefficient gain curve from theabove-discussed FIG. 5. Equation (18) is modified to return a fractionalAmbisonic order, which will be used by the encoder, as represented bythe following equation:n=13.15e ^(−2.74ϕ) ^(S)   (19)

To avoid changing the total output energy of a sound source whenchanging the source spread (e.g., desirable to ensure energypreservation), the sound object rendering device 300 not only appliesthe above-discussed gain ratio to the Ambisonic channels but also thetotal energy of the sound field when widening sound sources. Forexample, to preserve the total energy of the sound field, when using anAmbisonic order 4 in the system, the MaxRe coefficients for Ambisonicorder 4 would result in the narrowest source spread with a defaultamplitude. Similarly, by reducing the Ambisonic order, the sound sourceappears wider but also quieter.

To ensure that sources sound equally loud when their spread is changed,the sound object rendering device 300 compensates for lower (fractional)order MaxRe coefficients so that the sound source is equally loud, nomatter how wide it is. In some embodiments, to compute theenergy-preserving MaxRe coefficients, the sound object rendering device300 first computes the energy of the sound field at a given Ambisonicorder n, which corresponds to a desired source spread. The energy isnext compared to the energy of the sound field at the maximum Ambisonicorder N. Subsequently, the compensation gain γ_(n,N) is a square root ofthis ratio, as represented by the following equations:

$\begin{matrix}{E_{n,N} = {\sum_{i = 0}^{N}{\left( {{2i} + 1} \right)*{Max}\;{{Re}_{n,N}(i)}^{2}}}} & (20) \\{E_{N,N} = {\sum_{i = 0}^{N}{\left( {{2i} + 1} \right)*{Max}\;{{Re}_{N,N}(i)}^{2}}}} & (21) \\{\gamma_{n,N} = \sqrt{\frac{E_{N,N}}{E_{n,N}}}} & (22)\end{matrix}$

The energy-preserving set of MaxRe coefficients at an arbitrary sourceorder n in an Ambisonic system of order N, is represented by the raw setof MaxRe_(n,N) multiplied by the compensation gain γ_(n,N), asrepresented by the following equation:Max{circumflex over (R)}e _(n,N)=γ_(n,N)*MaxRe_(n,N)  (23)

The sound object rendering device 300 applies the MaxRe correctiondirectly to the binaural decoder using shelf-filters. This allows forsignificant performance improvements at run-time. Thus, theenergy-preserving MaxRe coefficients need to be further normalized sothat no correction is applied if the sound source spread is set to itsnominal (i.e., narrowest) value. This is achieved by dividing theenergy-preserving coefficients by the coefficients corresponding to themaximum Ambisonic order N, as represented by the following equation:

$\begin{matrix}{{{Max}\hat{\hat{R}}e_{n,N}} = \frac{{Max}\hat{R}e_{n,N}}{{Max}\;{Re}_{n,N}}} & (24)\end{matrix}$

The final set of energy-preserving, normalized MaxRe gain coefficientsare then pre-computed and written into a look-up table to be accessed atrun-time. Thus, the sound source spread correction gains are applied atrun-time.

In some embodiments, certain aspects of the techniques described abovemay be implemented by one or more processors of a processing systemexecuting software. The software comprises one or more sets ofexecutable instructions stored or otherwise tangibly embodied on anon-transitory computer readable storage medium. The software caninclude the instructions and certain data that, when executed by the oneor more processors, manipulate the one or more processors to perform oneor more aspects of the techniques described above. The non-transitorycomputer readable storage medium can include, for example, a magnetic oroptical disk storage device, solid state storage devices such as Flashmemory, a cache, random access memory (RAM) or other non-volatile memorydevice or devices, and the like. The executable instructions stored onthe non-transitory computer readable storage medium may be in sourcecode, assembly language code, object code, or other instruction formatthat is interpreted or otherwise executable by one or more processors.

A computer readable storage medium may include any storage medium, orcombination of storage media, accessible by a computer system during useto provide instructions and/or data to the computer system. Such storagemedia can include, but is not limited to, optical media (e.g., compactdisc (CD), digital versatile disc (DVD), Blu-Ray disc), magnetic media(e.g., floppy disc, magnetic tape, or magnetic hard drive), volatilememory (e.g., random access memory (RAM) or cache), non-volatile memory(e.g., read-only memory (ROM) or Flash memory), ormicroelectromechanical systems (MEMS)-based storage media. The computerreadable storage medium may be embedded in the computing system (e.g.,system RAM or ROM), fixedly attached to the computing system (e.g., amagnetic hard drive), removably attached to the computing system (e.g.,an optical disc or Universal Serial Bus (USB)-based Flash memory), orcoupled to the computer system via a wired or wireless network (e.g.,network accessible storage (NAS)).

Note that not all of the activities or elements described above in thegeneral description are required, that a portion of a specific activityor device may not be required, and that one or more further activitiesmay be performed, or elements included, in addition to those described.Still further, the order in which activities are listed are notnecessarily the order in which they are performed. Also, the conceptshave been described with reference to specific embodiments. However, oneof ordinary skill in the art appreciates that various modifications andchanges can be made without departing from the scope of the presentdisclosure as set forth in the claims below. Accordingly, thespecification and figures are to be regarded in an illustrative ratherthan a restrictive sense, and all such modifications are intended to beincluded within the scope of the present disclosure.

Benefits, other advantages, and solutions to problems have beendescribed above with regard to specific embodiments. However, thebenefits, advantages, solutions to problems, and any feature(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeature of any or all the claims. Moreover, the particular embodimentsdisclosed above are illustrative only, as the disclosed subject mattermay be modified and practiced in different but equivalent mannersapparent to those skilled in the art having the benefit of the teachingsherein. No limitations are intended to the details of construction ordesign herein shown, other than as described in the claims below. It istherefore evident that the particular embodiments disclosed above may bealtered or modified and all such variations are considered within thescope of the disclosed subject matter. Accordingly, the protectionsought herein is as set forth in the claims below.

What is claimed is:
 1. A method, comprising: receiving a set ofmonophonic sound inputs, wherein each of the set of monophonic soundinputs includes position and orientation information of a sound objectrelative to a source position; and encoding the set of monophonic soundinputs into a higher order ambisonic (HOA) sound field in a sphericalharmonics domain based on a spherical harmonics dataset that containsspherical harmonic coefficients for only a first sphere quadrant andbased on a symmetry relationship between the first sphere quadrant andat least a second sphere quadrant; and decoding the HOA sound field togenerate a set of loudspeaker signals.
 2. The method of claim 1, furthercomprising: convolving two or more of the generated set of loudspeakersignals and summing a left channel signal and a right channel signal togenerate a binaural sound output.
 3. The method of claim 1, furthercomprising: storing the spherical harmonics dataset as a sphericalharmonics lookup table.
 4. The method of claim 3, further comprising:computing the spherical harmonics lookup table prior to performing soundobject encoding.
 5. The method of claim 3, further comprising:determining a spherical harmonic coefficient of a second sphere quadrantbased on a corresponding spherical harmonic coefficient of the firstsphere quadrant from the spherical harmonics lookup table and based onthe symmetry relationship.
 6. The method of claim 1, further comprising:applying a gain correction to each of a plurality of Ambisonic channelsof the HOA sound field to change a source spread of the sound object. 7.The method of claim 6, further comprising: applying an energy-preservinggain correction to each of a plurality of Ambisonic channels of the HOAsound field to maintain a total energy level of the HOA sound field. 8.A sound object rendering device, comprising: a spherical harmonicsdataset including a subset of all spherical harmonic coefficients foronly a first sphere quadrant; and an encoder to receive a set ofmonophonic sound inputs, wherein each of the set of monophonic soundinputs includes position and orientation information of a sound objectrelative to a source position, and further wherein the encoder is toencode the set of monophonic sound inputs into a higher order ambisonic(HOA) sound field in a spherical harmonics domain based on the sphericalharmonics dataset and a symmetry relationship between the first spherequadrant and at least a second sphere quadrant.
 9. The sound objectrendering device of claim 8, further comprising: a rendering module todecode the HOA sound field to generate a set of loudspeaker signals, andwherein the rendering module is further to convolve two or more of thegenerated set of loudspeaker signals to generate a binaural soundoutput.
 10. The sound object rendering device of claim 8, furthercomprising: a shelf filter module to apply a gain correction to each ofa plurality of Ambisonic channels of the HOA sound field to change asource spread of the sound object.
 11. The sound object rendering deviceof claim 10, wherein the shelf filter module is further to apply anenergy-preserving gain correction to each of a plurality of Ambisonicchannels of the HOA sound field to maintain a total energy level of theHOA sound field.
 12. A non-transitory computer-readable storage mediumhaving stored thereon instructions that, when executed, cause one ormore processors to: receive a set of monophonic sound inputs, whereineach of the set of monophonic sound inputs includes position andorientation information of a sound object relative to a source position;encode, based on a spherical harmonics dataset including sphericalharmonic coefficients for only a first sphere quadrant and based on asymmetry relationship between the first sphere quadrant and at least asecond sphere quadrant, the set of monophonic sound inputs into a higherorder ambisonic (HOA) sound field in a spherical harmonics domain; anddecode the HOA sound field to generate a set of loudspeaker signals. 13.The non-transitory computer-readable storage medium of claim 12, whereinthe one or more processors is further to: convolve two or more of thegenerated set of loudspeaker signals and summing a left channel signaland a right channel signal to generate a binaural sound output.
 14. Thenon-transitory computer-readable storage medium of claim 12, wherein theone or more processors is further to: store the spherical harmonicsdataset as a spherical harmonics lookup table.
 15. The non-transitorycomputer-readable storage medium of claim 14, wherein the one or moreprocessors is further to: compute the spherical harmonics lookup tableprior to performing sound object encoding.
 16. The non-transitorycomputer-readable storage medium of claim 15, wherein the one or moreprocessors is further to: compute the spherical harmonics lookup tableby computing the first sphere quadrant of all spherical harmoniccoefficients.
 17. The non-transitory computer-readable storage medium ofclaim 16, wherein the one or more processors is further to: determine,based on a symmetry look-up table representing the symmetryrelationship, a spherical harmonic coefficient of the second spherequadrant from a corresponding spherical harmonic coefficient from thespherical harmonics lookup table.
 18. The non-transitorycomputer-readable storage medium of claim 12, wherein the one or moreprocessors is further to: applying a gain correction to each of aplurality of Ambisonic channels of the HOA sound field to change asource spread of the sound object.
 19. The non-transitorycomputer-readable storage medium of claim 18, wherein the one or moreprocessors is further to: apply an energy-preserving gain correction toeach of a plurality of Ambisonic channels of the HOA sound field tomaintain a total energy level of the HOA sound field.
 20. A sound objectrendering device, comprising: a spherical harmonics dataset includingspherical harmonic coefficients; an encoder to receive a set ofmonophonic sound inputs, wherein each of the set of monophonic soundinputs includes position and orientation information of a sound objectrelative to a source position, and further wherein the encoder is toencode the set of monophonic sound inputs into a higher order ambisonic(HOA) sound field in a spherical harmonics domain based on the sphericalharmonics dataset; and a shelf filter module to apply at least one of: again correction to each of a plurality of Ambisonic channels of the HOAsound field to change a source spread of the sound object; and anenergy-preserving gain correction to each of a plurality of Ambisonicchannels of the HOA sound field to maintain a total energy level of theHOA sound field.